Direct evaluation of the equivalent linear damping for TLCD systems in random vibration for pre-design purposes

• An approximate formulation for TLCD systems under random loads is introduced.
• The proposed formulation is useful for design purposes, avoiding iterations.
• Its validity is assessed by Monte Carlo simulations on the non-linear system.
• Parametric analyses are carried out to define the parameters range of applicability.
• The proposed formulation can be used in an optimization framework.

Passive control of structural vibrations has received in recent years a great attention from researchers concerned with vibration control. Several types of devices have been proposed in order to reduce the dynamic responses of different kinds of structural systems. Among them, the Tuned Liquid Column Damper (TLCD) proved to be very effective in reducing vibration of structures. Since the increasing use of TLCDs in practical realizations, this paper aims at developing an approximate formulation, by means of a statistical linearization technique, able to estimate the parameters of a structure equipped with a TLCD subjected to random loads for pre-design purposes. Moreover, it is shown that results obtained via Monte Carlo approach on the non-linear system are in good agreement with those obtained by means of the proposed formulation.